Do you know which conifer you have? That will make a difference as to it's attainable height. It takes some clematis to get going & depending on what you have may make a difference. PC is pruning 2 & VdL is 3, read the other thread as to how that can be a difference & decide from there. Once you make a decision about how you feel about type 2 or 3 & figure out the conifer you have, it will be a lot easier to answer. I am in the same zone as you, so if you need help IDing it, I will do my best.

Yes, you could plant a clematis on a 6' evergreen. The vines you picked should be fine. You can always pinch them back to keep them smaller, or have the vines grow back down the tree when it gets to the top. Those varieties should not overwhelm the tree. Just don't plant a huge SAC or Montana,etc., as that would get too big. You will need to give the clematis extra water and fetilizer as the evergreen's roots will compete with the clematis. I have many clematis on evergreens and it works just fine.

Not all conifers are created equal. I have a few that it would never work on. Pinus reflexa, they call it reflexa for a reason, I can literally tie the branches in a knot if I wanted to & no way would it support a clem. I have a Skyrocket Juniper I would never plant one on either because the branches are long & growing completely upright & it would be a splayed out fool if I tried growing a clem up it & those are 7' x 2.5'.

I would still contemplate putting a type 2 on a conifer unless you treat it as a 3.